You can find the Ubercart invoice email template files @ sites/all/modules/ubercart/uc_order/templates. You could copy and edit the uc-order–customer.tpl.php to fit your needs but you could not select it @ E-mail customer checkout notification > Email an order invoice in Rules. This is because you have to implement the hook_uc_invoice_templates() before the new template is selectable.
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